A343270 Number of partitions of n into 3 parts x,y,z such that (x+y+z) | x*y*z.

0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 3, 0, 3, 4, 5, 0, 6, 0, 6, 6, 5, 0, 11, 2, 6, 7, 9, 0, 23, 0, 11, 10, 8, 12, 15, 0, 9, 12, 21, 0, 34, 0, 15, 19, 11, 0, 41, 4, 18, 16, 18, 0, 36, 20, 31, 18, 14, 0, 61, 0, 15, 28, 33, 24, 56, 0, 24, 22, 65, 0, 48, 0, 18, 32, 27, 30, 67, 0, 77

Offset: 1

Author

Wesley Ivan Hurt, Apr 09 2021

Keywords

• nonn

Examples

			a(9) = 1; [3,3,3];
a(10) = 2; [1,4,5], [2,3,5];
a(11) = 0;
a(12) = 3; [1,3,8], [2,4,6], [3,4,5].
		

Links

• Index entries for sequences related to partitions

Programs

Mathematica

Table[Sum[Sum[(1 - Ceiling[i*j*(n - i - j)/n] + Floor[i*j*(n - i - j)/n]), {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 100}]

Formula

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1 - ceiling(i*j*(n-i-j)/n) + floor(i*j*(n-i-j)/n)).